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free energy curves
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Image
Published: 01 March 2012
Fig. 3.19 (a) Molar free-energy curve for the α phase. (b) Molar free-energy curves for α and β. Adapted from Ref 3.1
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Image
Published: 01 December 2008
Fig. 3.9 Free-energy curves for an ideal solution and a regular solution of A-B binary system. (a) Ideal solution, Ω AB = 0. (b) Solution with Ω AB < 0 (c) Solution with Ω AB > 0. A concave region appears at the temperature below T C = Ω AB /2 R (see section 4.4 ).
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Published: 01 March 2012
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Published: 01 March 2012
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Published: 01 June 2008
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Published: 01 June 2008
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Published: 01 June 2008
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Published: 01 June 2008
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Published: 01 December 2008
Fig. 3.11 Composition and free-energy curve of a complex oxide (Al, Cr) 2 O 3 . (a) Composition of (Al, Cr) 2 O 3 . (b) Free-energy curve of Al 2 O 3 -Cr 2 O 3 pseudobinary system (schematic illustration)
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Published: 01 March 2012
Fig. 3.11 The relationship between the free-energy curve for a solution and the chemical potentials of the components. Adapted from Ref 3.1
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Published: 01 March 2012
Fig. 9.17 Free-energy curve illustrating change in chemical potential with composition. Source: Ref 9.9 as published in Ref 9.10
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Book Chapter
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2012
DOI: 10.31399/asm.tb.pdub.t53420041
EISBN: 978-1-62708-310-2
... energies and chemical potentials, and shows how the equilibrium state of an alloy can be obtained from free-energy curves. binary solid solutions chemical potential Gibbs free energy interatomic bonds phase diagrams single-component systems thermodynamics THERMODYNAMICS is a branch...
Abstract
This chapter explains how the principles of chemical thermodynamics are used in the construction and interpretation of phase diagrams. After a brief review of the laws of thermodynamics, it describes the concept of Gibbs free energy and its application to transformations that occur in single-component and binary solid solutions. It then examines the relationship between the free energy of a solution and the chemical potentials of the individual components. It also explains how to account for the heat of mixing using quasi-chemical models, discusses the effect of interatomic bond energies and chemical potentials, and shows how the equilibrium state of an alloy can be obtained from free-energy curves.
Book Chapter
Series: ASM Technical Books
Publisher: ASM International
Published: 01 June 2008
DOI: 10.31399/asm.tb.emea.t52240075
EISBN: 978-1-62708-251-8
.... The major eutectic systems include the aluminum-silicon eutectic system and the lead-tin eutectic system. The chapter discusses the construction of eutectic phase diagrams from free energy curves. It also provides information on peritectic, monotectic, and solid-state reactions in alloy systems...
Abstract
Phase diagrams are graphical representations that show the phases present in the material at various compositions, temperatures, and pressures. This chapter begins with a section describing the construction of phase diagrams for the simple binary isomorphous system. A binary phase diagram can be used to determine three important types of information: the phases that are present, the composition of the phases, and the percentages or fractions of the phases. The chapter then describes the construction of one common type of binary phase diagram i.e., the eutectic alloy system. The major eutectic systems include the aluminum-silicon eutectic system and the lead-tin eutectic system. The chapter discusses the construction of eutectic phase diagrams from free energy curves. It also provides information on peritectic, monotectic, and solid-state reactions in alloy systems. The presence of intermediate phases is also described. Finally, a brief section provides some information on ternary phase diagrams.
Image
Published: 01 March 2012
Fig. 16.9 (a) Gibbs free-energy composition diagram and (b) locus of solvus curves of metastable and stable equilibrium phases in a precipitation sequence. (a) The points of common tangency show the relationship between compositions of the matrix phase (C″, C′, and C eq ) and the various forms
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Image
Published: 01 March 2012
Fig. 16.12 Free-energy plots of precipitation sequence in aluminum-copper alloys. (a) Free-energy curve with common tangent points for phase compositions in the matrix. (b) Step reductions in the free energy as the transformation proceeds. C eq and C 3 , copper content of α eq and α 3
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Published: 01 December 2008
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Published: 01 December 2008
Fig. 4.1 Conditional equations of heterogeneous equilibrium in a unitary (a) and a binary (b) system. (a) Intersection of free-energy curves is the equilibrium temperature in a unitary system. (b) Points of contact ① and ② on the common tangent indicate each
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Book Chapter
Series: ASM Technical Books
Publisher: ASM International
Published: 01 June 2008
DOI: 10.31399/asm.tb.emea.t52240053
EISBN: 978-1-62708-251-8
... , and in newer texts, the same free-energy curves are now identified with the Gibbs free energy, G . However, what is really important in metallurgical processes is not the free energy, G , itself, but the change in free energy, Δ G . It can be shown that, at constant temperature and pressure: (Eq 4.6) Δ...
Abstract
This chapter provides a short introduction to phase transformations, namely, the liquid-to-solid phase transformations that occur during solidification and the solid-to-solid transformations that are important in processing, such as heat treatment. It also introduces the concept of free energy that governs whether or not a phase transformation is possible, and then the kinetic considerations that determine the rate at which transformations take place. The chapter also describes important solid-state transformations such as spinodal decomposition and martensitic transformation.
Book Chapter
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.tb.tm.t52320091
EISBN: 978-1-62708-357-7
... materials are explained. 4.1 Basic Rules of Heterogeneous Equilibrium 4.1.1 Common Tangent Law For phase I and II of a one-component system (pure substance A) to be in equilibrium, as in Fig. 4.1(a) , free-energy curves of both phases, G A I and G A I I...
Abstract
This chapter explains the significance of the phase diagram and its use in the development of new materials. The chapter describes the basic rules of heterogeneous equilibrium, presents a comparison between liquidus line and solidus line, and provides information on the solubility curve and the binodal curve.
Book Chapter
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2012
DOI: 10.31399/asm.tb.pdub.t53420015
EISBN: 978-1-62708-310-2
... G L < 0 Fig. 2.12 Gibbs free-energy curves during solidification. Source: Ref 2.2 Immediately below T m , the free-energy change is very small, so solidification occurs slowly, but at larger undercooling or supercooling ( T m – T ), the free-energy change becomes...
Abstract
This chapter describes the physical characteristics, properties, and behaviors of solid solutions under equilibrium conditions. It begins with a review of a single-component pure metal system and its unary phase diagram. It then examines the solid solution formed by copper and nickel atoms. It discusses the difference between interstitial and substitutional solid solutions and the factors that determine the type of solution that two metals are likely to form. It also addresses the development of intermediate phases, the role of free energy, transformation kinetics, liquid-to-solid and solid-state phase transformations, and the allotropic nature of metals.